# Finding coordinates given 3-dimensional vectors

## Homework Statement

\begin{align*} \vec{u} = 2 \hat{x} - 3 \hat{y} + \hat{z} \vec{v} = \hat{x} - \hat{y} - \hat{z} \end{align*}

Given a parallelogram that's vertex is at the origin (0,0,0) and is created by two vectors u and v:

a) find where the fourth vertex is of the parallelogram
b) find the length of the two diagonals

## The Attempt at a Solution

a) since it's a parallelogram, the fourth point is at u + v = $$3 \hat{x} - 4 \hat{y}$$ ------- I'm not sure if the answer is supposed to be in this form or in form (3,-4,0)

b) I'm not sure about this one. By length, do they mean distance? Should I use the distance formula between two points? Or do they possibly mean vector addition/subtraction?

Thanks!

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## Answers and Replies

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Hi mysmyst.

a) The vector u+v points to the fourth vertex, whose coordinates are (3,-4,0)

b) You may calculate the vectors that follow the diagonals, from u and v, and then calculate their modules.

the big diagonal is obviously u+v. but is the little diagonal u-v or v-u? and how do I tell which it is in general?

Thanks!

The little diagonal is (v-u) and also (u-v). It doesn't matter. It depends on which sense you see it.

o. that was silly (:

Thanks!

is there a thanks button?